As is generally known, in order to attain both a reduction in the amount of nitrogen oxides (NOx) produced by an internal combustion engine, based on an increase in inert gases contributing to a reduced combustion temperature, and a reduction in pumping loss contributing to a reduced fuel consumption, a spark-ignition internal combustion engine often uses a variable valve operating mechanism so as to actively increase a valve overlap that the open periods of intake and exhaust valves are overlapped, and consequently to increase the amount of internal EGR. In such a case, it is more desirable to simultaneously optimize or compensate for an ignition timing, a fuel-injection amount, a valve open timing and a valve closure timing of at least one of intake and exhaust valves, and the like, responsively to a change in internal EGR. One such internal EGR estimation method has been disclosed in Japanese Patent Provisional Publication No. 2001-221105 (hereinafter is referred to as “JP2001-221105”). According to the internal EGR estimation method of JP2001-221105, a basic value of internal EGR, corresponding to the amount of burned gas remaining in the engine cylinder under a non-overlapped condition of the open periods of intake and exhaust valves, is calculated based on engine operating conditions such as engine load, engine speed, an air/fuel mixture ratio (A/F), an EGR ratio of the amount of exhaust gas recirculated to the total gas amount per cylinder, and an intake-manifold pressure. During the valve overlap, the estimate of internal EGR is increasingly compensated for by adding a valve-overlap correction value, which is based on a valve overlap period, a phase of a central crank angle between the beginning-of-valve-overlap crank angle and the end-of-valve-overlap crank angle, and intake-manifold pressure, to the basic value of internal EGR calculated. However, in particular in a transient engine operating state that at least one of the engine load, engine speed, air/fuel mixture ratio, and intake-manifold pressure remarkably varies, it is difficult to univocally exactly estimate the amount of internal EGR from the valve overlap period. Thus, it is desirable to more precisely estimate the amount of internal EGR depending on variations in engine operating conditions.
Additionally, under particular engine operating conditions, such as just after starting with a cold engine, just after deceleration fuel-cutoff operating mode, or at high-speed high-load operation during which engine coolant temperature is very high, a valve clearance itself tends to remarkably change owing to thermal expansion of the engine valve and shaft in the valve operating mechanism, arising from temperature changes in the valve and the cylinder head and cylinder block. This causes a deviation of the actual valve overlap period from a desired valve overlap, in other words, a deviation of the actual internal EGR amount from a desired internal EGR amount computed based on the engine operating conditions. Such a deviation lowers the control accuracy of the electronic ignition timing control system and/or the electronic fuel injection control system, and thereby results in the deteriorated vehicle drivability, increased fuel consumption, and lowered exhaust-emission performance.